Why does this happen when using subdivision modifier?
This can have multiple reasons, mean crease has this effect but it's not purple on the edge so I exclude it. "doubles" is another possibility, the most likely one. Doubles is what we blenderers refer to when multiple vertices or points are on the same location.
This can be caused by loop cuts that you have placed on other places and not noticed how it went around there too or when you extruded, but then rigth clicked it and forgot about it.

Luckily there is an easy fix for that.

It seems like you are using blender 2.8. I am not sure how your settings are but if you press space bar you can search for "merge by distance" in older blender versions this was known as "remove doubles". It will, what the name suggests, merge vertecies by their distance to each other. But if you do so make sure you don't accedentally get unwanted triangles, which can happen when it was a loop cut that went around the without you noticing.